Regularizing Effect of Two Hypotheses on the Interplay Between Coefficients in Some Hamilton–Jacobi Equations

We study of the regularizing effect of the interaction between the coefficient of the zero-order term and the lower-order term in quasilinear Dirichlet problems whose model is where Ω is a bounded open set of , is a Carathéodory matrix on which is elliptic (that is, for every ) and bounded (that is, for every ), , and . We prove the existence of a weak solution belonging to and to when either or In addition, we also prove the existence for every and satisfying both conditions (0.1) and (0.2) jointly.